How to Waste a Crisis: Budget Cuts and Public Service Reform David Hugh-Jones 22/07/10

Abstract In the aftermath of the financial crisis, governments have proclaimed their intention to find efficiency savings by reforming government bureaucracy. However, this paper identifies a conflict between savings and reform. Governments are uncertain which departments are effective. In normal times, effective departments can be identified by increasing their budget for a trial period. They will then be able to do more than ineffective ones with the extra money. In bad times, however, the government cannot afford to expand the budget. Then, ineffective departments can mimic effecitve ones simply by reducing their effort. An empirical implication is that less effective departments will be more affected by budget cuts. This prediction is confirmed in a panel of 9965 US libraries. A second implication is that during fiscal crises, politicians will increase control and oversight of the bureaucracy.

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Keywords: bureaucracy, reform, signaling As government borrowing ballooned of the financial crisis of 2008, an era of deficit reduction and tight budget constraints loomed. But political figures around the world looked for the silver lining. Rahm Emmanuel remarked: “You never want a serious crisis to go to waste” (Seib, 2008). Hillary Clinton told young Europeans: “Never waste a good crisis” (Independent, 2009). And Barack Obama exhorted the American nation “to discover great opportunity in the midst of great crisis” (USAToday, 2009). On the other side of the pond, management consultants urged the public sector to “us[e] the downturn as a catalyst” to “embrace innovation and rethink delivery models” (Deloitte, 2009), while David Cameron described public service modernization as “not an alternative to dealing with our debts - it’s a key part of it” (Cameron, 2011). These inspiring slogans are capable of multiple interpretations, but one central one, best expressed by the Cameron quote, is that periods of austerity are the right times for reform. Ordinarily, politicians face few incentives to examine public sector budgets for waste and inefficiency. When budgets are constrained, however, they need to inspect the books more closely, trim dead wood programs, and emerge with a slimmer but more effective government. This paper explores these issues, with the aim of extending our comprehension of the relationship between budget constraints and efficient allocations. It gives one reason why the hopes expressed above may not be borne out. In the model presented here, savings do not, in general, promote efficiency. Instead, there is a trade-off between savings and efficiency, which bites particularly hard when budgets are tight. The logic is one of signalling. Governments are unsure a priori 2

which departments are spending public money effectively. In good times, a government can identify effective departments by increasing their budget on a trial basis. Efficient departments will then be able to do more than inefficient ones with the extra money. In bad times, however, the government cannot afford to expand the budget. It would like to cut the budget of ineffective but over-resourced departments, whose output will be least affected by the cuts. But such departments cannot be identified by trial cuts, because by working inefficiently, they can make it appear that any cut is very harmful. The argument is illustrated below in Figure 1. The x axis measures a bureaucratic department’s budget. The y axis measures the department’s output – a (presumably public) good such as miles of roads maintained, library books lent out, or heart operations performed. A government in office observes a single point in these two dimensions: the current budget and the current output. From the government’s point of view, this is the point where a set of counterfactual lines cross. In other words, decision-makers must answer the question: “what would happen if we raised, or cut, this department’s budget?” Correspondingly, the bureaucratic departments is one of two possible kinds.1 It may be a high marginal productivity type (“high type” for short), whose output will be increased a lot by extra money, and be harmed a lot by cuts. Or it may be a “low” marginal productivity type, which will gain less from extra cash and be harmed less by cuts. Ex ante, there is no reason that the potential output curves of the two types should cross precisely at the current budget; instead, we can imagine a larger set of possible types, of which only these two are compatible with the observed status quo budget and 1 The

simplifying assumption of two types is used throughout; the logic extends trivially to a continuum of types.

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output. Departmental productivity could differ in this way for many reasons. Departments may vary both in their efficiency, and simultaneously face tasks and external environments of varying difficulty. Or, the social value of the task they do may be uncertain; some aspects of the task are highly valuable, others less so, and it is hard to untangle these. Since the government may not be able to observe all these factors, it may be unsure of the effects of changes to the budget. However, I assume that the government does have reasonable information about the department’s current performance. So, for example, the government may know how many miles of road were built in the current year, but be less sure about how many miles could be built with a 10% increase or cut in the budget: exactly how much can costs be driven down in negotiations with contractors? Or, reliable crime figures may be recorded, but it may be unclear how they would be affected by an increase or cut in the budget for policing. These assumptions exclude, on the one hand, bureaucratic activities whose value is intrinsically hard to measure, such as public funding of the arts, or activities whose outputs are not immediately experienced, such as children’s education; and on the other hand, activities with clear outputs that are also offered in competitive markets at public prices, such as perhaps the purchase of IT equipment or stationery. In forming estimates of potential outputs for different budgets, governments may have more history to go on than a single data point. However, since bureaucratic capacities, external conditions and the social value of outputs all change over time, the government will still face some uncertainty over the bureaucracy’s production 4

possibility frontier; this uncertainty will be lowest for relatively recent data; and, since most budget changes are incremental, this data will probably involve budget inputs close to the current one. For simplicity, I therefore assume that output at the current budget is known for sure, with uncertainty increasing as we move farther from this point. Suppose that the long-run cost of the government’s funds is given as in the curved line in the picture. Then, the optimal budget for a high type department would be at point B, where marginal benefit is equal to marginal cost – an increase on the current budget. The optimal budget for a low type department would be a cut to point A. One way to find out the quality of the department would be to increase the budget for a short time, for example to point B itself. Suppose that the bureaucracy is a single actor, who can costlessly produce any output up to the line for the department’s type, and who is solely interested in maximizing the departmental budget à la Niskanen (1971).2 With the extra cash, a high type department can produce strictly higher output than the low type department could. By doing so, the bureaucrat can demonstrate the department’s competence and continue to receive a higher budget in future. A low type department, on the other hand, can only produce up to its output line. After the trial period, efficient long-term budget allocations can be made, according to the department’s type, at either A or B. Now, however, suppose that the government faces a tight short-run budget constraint. For example, it may have entered office with high government borrowing left over from the previous administration, and bond markets nervous about its 2 This

is a simplification (Dunleavy, 1985), but perhaps not an unrealistic one, if interpreted within the context of protecting an existing budget from cuts.

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Figure 1: Bureaucratic departments

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ability to repay. Or, a particular minister may have been allocated a low budget by the Prime Minister. Say that the maximum budget available for the trial period is below the crossing point of the departments’ output lines. The situation is now very different, because a high type department can no longer perform better than a low type department could. Since the high type’s marginal productivity at current output is higher, it will be more affected by the budget cut. Even when the high type performs at its maximum, the low type can match it by costlessly lowering its output. In other words, over-resourced bureaucrats can claim that they are more harmed by budget cuts than they really are, simply by reducing their productivity. As a result, in the long run, departments cannot be distinguished and the budget allocation will be inefficient. The idea that bureaucrats may respond to budget cuts by exaggerating their effects, or even by deliberately making their effects worse, is part of the folk wisdom of public administration. The tactic is known as “sore thumbs”, “bleeding stumps”, or in the US as the Washington Monument Ploy, named after the US Park Service’s regular threats to close the Washington Monument if their budget were to be cut. Wildavsky (1979 [1964] p.102) mentions “cut the popular program” as a strategy for agencies seeking to reverse budget cuts. Several authors in Hood and Wright (1982) describe the bleeding stumps tactic; as the editors put it, “the course of retrenchment is fatally distorted by bureaucratic preferences”. The current round of post-crisis budgets has led to other examples. In 2008, California governor Arnold Schwarzenegger rhetorically proposed a budget which included the early release of 37,000 prisoners. Eric Pickles (the current Secretary of State for Communities and Local Government) has accused Labour local authorities of

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operating a “bleeding stumps strategy” ?. However, the distortions of retrenchment go beyond the direct effects of shirking by ill-motivated bureaucracies. At least as important is the information loss because the government – the principal in this situation – cannot identify the truly essential programs, where cuts will seriously harm the provision of public services. While the loss from shirking is immediate, the information loss is more long-term and may outlast the crisis period. And, of course, the information loss occurs even when the bureaucracy is not shirking at all, but is genuinely damaged by cuts. The theory here also clarifies why stories of “bleeding stumps” emerge in times of cutbacks and not of growth: the Washington Monument ploy can be used when the government must cut spending, but there is no corrresponding tactic for when budgets are going up. Below the model is developed in detail. The empirics examine a panel of US libraries. The data support a key prediction of the model: that less effective bureaucracies will be more likely to underperform in years when their budget is cut, while more effective bureaucracies will be less affected by budget cuts.

Model There is a single bureaucracy, which is either a high-productivity type, or a lowproductivity type. Given a budget of x, the high type produces output to the value of αH + βH x, while the low type produces αL + βL x with βL < βH . Current spending is at a default level x¯ and output is y, ¯ where y¯ = αH + βH x¯ = αL + βL x¯ is the point at which both lines cross. This is not a coincidence: the government’s observation of current productivity can be thought of as reducing its uncertainty over the production function, perhaps from a much larger space of types. 8

Rather than imposing a hard budget constraint as above, I assume the government faces a short-term cost of funds c(x) ˆ = kc(x). Marginal cost is increasing, since the government’s credit in the markets is not unlimited, and since there are competing spending priorities. The parameter k reflects how these conditions may vary. When there are many competing priorities and funds are tight, or when the government must pay high interest to borrow, k will be high. I assume c0 , c00 > 0, c(0) = 0 and c0 (x) → 0 as x → 0. The long-term cost of funds is normalized at k = 1. The timing is as follows: 1. Nature draws the bureaucracy’s type τ ∈ {H, L} which is high (H) with probability π. 2. The government chooses a first-period budget x1 at a cost kc(x1 ). 3. The bureaucracy chooses a level of output y1 ≤ ατ + βτ x1 . Inefficient levels of output y1 < ατ + βτ x1 may be achieved by, for example, allocating funds to inefficient uses. 4. The government observes y1 and chooses a second-period budget x2 at a cost c(x2 ). 5. The bureaucracy produces y2 ≤ ατ + βτ x2 . We assume in fact that in the second period the bureaucracy produces efficiently at y2 = ατ + βτ x2 .3 6. Payoffs are realised. The bureaucracy receives δ x1 + x2 and the government’s utility is δ [y1 − kc(x1 )] + y2 − c(x2 ). Here δ is a parameter reflecting 3 This

would be guaranteed if, for example, destroying output had a small (second-order) cost.

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the relative length of the first period, in other words the time until output becomes accurately measurable. This time may be greater for some outputs than for others.

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We first look for conditions in which the government can distinguish the types after the first period. If this is so, the second period budget will be xH solving c0 (xH ) = βH for a high type and xL solving c0 (xL ) = βL for a low type. Since xH > xL , each type of bureaucracy would prefer to appear like the high type. For x1 ≤ x, ¯ because the low type’s maximum possible output exceeds the high type’s, the low type can match any output that the high type could produce. Thus it must be that x1 > x. ¯ Then the high type bureaucracy can exceed any possible output of the low type, and so identify itself to the government, by producing efficiently. So for a high enough first period budget, types can always be distinguished. However, if the short-run cost of funds is large, the government may prefer not to do so. The short-run optimum budget allocation, ignoring the second period and assuming that both types of bureaucrat produce efficiently, would be x1∗ solving c0 (x1∗ ) =

πβH + (1 − π)βL . k

If x1∗ > x¯ then the short-run optimum will also allow the government to distinguish the types. But if k is large enough this will no longer hold. The government then faces a choice: keep the budget high in the first period in order to observe the bureaucracy’s type, or spend less and fail to do so. 4 For

instance, the effectiveness of infrastructure investment may take longer to become clear than the effectiveness of hardship payments to Old Age Pensioners. Recent British governments have invested extensively in performance management statistics for local authorities, health and education.

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Keeping the budget high requires allocating x1 = x¯ in the first period5 . The government’s expected total payoff is then

δ [y¯ − kc(x)] ¯ + π(yH − c(xH )) + (1 − π)(yL − c(xL ))

where yτ = ατ + βτ xτ is type τ’s output after an optimal choice of period 2 budget. Alternatively, the government could spend less than x. ¯ If so, then in equilibrium both types will produce the same output. For, if not, the low type could pool with the high type by changing output, and would then increase its period 2 budget. I assume that for x1 < x, ¯ the high type produces efficiently and the low type matches it. As a result the government’s total payoff will be δ [αH + βH x1 − kc(x1 )] + π(αH + βH x2∗ ) + (1 − π)(αL + βL x2∗ ) − c(x2∗ )

(1)

where x2∗ solves the second period first order condition c0 (x2∗ ) = πβH + (1 − π)βL .

Optimizing over x1 , observe that the government should treat the bureaucracy like a high type, since the low type will pool at the same output. Thus the optimal choice xˆ1 solves c0 (xˆ1 ) = βH /k. 5 In

fact, to learn the department’s type we require x1 > x. ¯ This open set has no minimum, so the government’s optimal choice may not be well-defined. This is a purely technical point, and I simply assume that the government must pay some arbitrarily small extra amount above x¯ to differentiate the types. An alternative fix would be to add some noise to the department’s output. In this case, larger budget increments above x¯ would give continuously more accurate signals of deparmental type, and the optimal budget would trade off signal accuracy against period 1 optimality, typically coming in strictly above x. ¯

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Comparing the two alternatives, the net benefit of choosing x¯ can be split into two components. There is a period 1 negative gain of

δ [βH (x¯ − xˆ1 ) − k(c(x) ¯ − c(xˆ1 ))].

(2)

This is negative, and decreasing (without bound) in k and δ .6 On the other hand there is a period 2 gain from knowing the types, of π[βH (xH − x2∗ ) − (c(xH ) − c(x2∗ ))] + (1 − π)[βL (xL − x2∗ ) − (c(xL ) − c(x2∗ ))]

This is positive and unrelated to δ or k. Summing these gains, if δ or k is high enough, then the government will strictly prefer to choose xˆ1 in period 1, enacting a budget cut which weakens its ability to distinguish an effective from an ineffective department.

Empirics: behaviour of the bureaucracy One implication of this theory is that governments’ budget allocations do not decrease continuously as the cost of funds k increases. Instead, at first the government prefers to keep funding steady, so as to learn about the bureaucracy; a further increase in k leads to a discontinuous drop in the budget when maintaining the existing level can no longer be afforded. Another implication is that productivity decreases after budget cuts. However, both these predictions are already made by extant theories: budget cuts may harm bureaucratic morale (Hood and Wright, 6 Shown

in the Appendix.

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N8 # unique library systems # years data per library Income ($) % change income Attendance Circulation Public Service Hours

Min 1 504 -99.7% 1 0 0

Median 12 369,900 5.0% 68,790 102,400 2,938

91687 6695 Mean 9.2 1,410,000 8.5% 211,800 329,200 5,583

Max 17 249,700,000 114.3% 17,940,000 23,240,000 250,400

Table 1: US Public Libraries Survey, descriptive statistics 1982); budget-setters may use the status quo as a reference point (Wildavsky, 1964b); and so forth. A more specific implication of the model is that high- and low-productivity departments will be affected differently by budget cuts. Highproductivity departments will produce no less output after a budget cut than in normal times. Low-productivity departments will produce less, since they will pool with high-productivity departments. To test this prediction, I examine data from the US Public Libraries Survey, covering 9965 US public library systems7 over the time period 1993 to 2009. Libraries are a plausible case for the theory. First, they produce measurable outputs – books lent, total visits and inter-library loans serviced – which are recorded in the survey data. Second, the “bleeding stumps” tactic appears to be known in the sector: library management textbooks mention it as a potential method of avoiding budget cuts (e.g. Wood and Young, 1988). Table 1 shows descriptive statistics for this dataset. The Public Libraries Surveys include budget data, and also data on various outputs, including attendance, circulation, and total annual Public Service Hours 7A

public library system is a single managerial and accounting unit, which may comprise one or more physical branches.

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(summed over all library branches). I use Public Service Hours (PSH) as the main measure of output, since these should be least affected by variation in consumer demand. To get an intuition for the empirics, consider Figure 2. Each figure plots logged yearly PSH against logged yearly budget for a single library in the dataset. The straight line is the result of a regression using only those years when the library’s (nominal) budget increased. Triangles show years when the budget decreased. For Viking Library System Operations, Minnesota, the line is relatively steep: in the model’s terminology, this library could be a “high type”. Correspondingly, in 3 out of 4 years of budget cuts, attendance was higher than the regression predicts. For Ypsilanti District Library, Michigan, by contrast, the line is not merely shallow but negatively sloped: the library achieved fewer Public Service Hours when its budget was larger. This is a “low type”. In 3 out of 4 years when its budget was cut, the Ypsilanti library performed worse than the prediction from the regression. As the model predicts, the less productive library underperformed when the budget was cut; the more productive library did not. To repeat this analysis for the entire dataset,9 I ran the following procedure for each library: 1. Regress log PSH on log income, using only years in which income increased. 2. Examine the difference between real PSH and PSH predicted from this regression (i.e. the residuals), for all “cutback years” in which income de9I

used every library with at least 12 years of data during which the budget increased, and at least one year during which the budget decreased.

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(a) Viking Library System Operations, Minnesota

(b) Ypsilanti District Library, Michigan

Figure 2: Public Service Hours versus budget, for two libraries 15

creased. 3. Record the slope of PSH on income, and the proportion of residuals which were negative. My hypothesis is that in cutback years, low marginal productivity libraries will be more likely to have lower-than-predicted public service hours, where marginal productivity is measured by the slope of PSH on library income. Figure 3 plots marginal productivity (i.e. the slope of the PSH-income regression) against the proportion of cutback years in which actual hours were fewer than predicted (ie of cutback years with negative residuals). As predicted, the more productive libraries, with the higher slopes, had fewer negative residuals in years of budget decrease (Kendall’s test of correlation: p < 0.001). Figure 4 shows the same data aggregated by deciles of productivity. The size of the effect is quite substantial: the least productive libraries underperformed in around 60% of cutback years, while the most productive libraries underperformed in around 40% of cutback years. As a robustness check I repeated the analysis using a quadratic in log income, measuring the PSH-income slope at the mean of the library’s log income. Results were substantively unchanged (Kendall’s test of correlation: p < 0.001). I also reran the analysis using all libraries with at least 6 years when the budget increased, and again results were robust (Kendall’s test of correlation: p < 0.001). Lastly I repeated the basic analysis on subsets of the data. The relationship between productivity and underperformance during cutbacks was negative in 39 out of the 47 states for which enough measurements were available. It also held in every decile of library size, as measured by total income in 2000, was significant 16

Figure 3: Library productivity versus performance during cutbacks

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Figure 4: Library productivity versus performance during cutbacks: by decile

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at p < 0.05 (Kendall’s test) in 9 out of 10 deciles, and was always significant at p < 0.10.

Empirics: behaviour of the budget-setter A further prediction of the model focuses on the government’s behaviour. In normal times, the department’s first period output informs the government of the department’s type, and the government allocates a larger budget to more productive departments. After cutbacks, however, first period output is no longer informative and the government ignores it in setting the second period budget. The US libraries in the PLS dataset receive on average about 77% of their income from local governments, with about 10% coming from state governments. I examine how the libraries’ total income is affected by their short-run output elasticity in the previous two years, defined as

% change in total service hours , % change in budget over years t − 2 and t − 1. Elasticity will be high if the library increases total service hours in response to a budget increase, or if it decreases total service hours in response to a budget cut: in other words it is a short-run estimate of marginal productivity (in the model’s terms, of the library’s type). The dependent variable is percentage change in budget in year t. If governments indeed learn more from, and react more to, recent performance during normal years than cutback years, then the coefficient of elasticity upon budget change will be larger during normal years. Table 2 shows the results. 19

Table 2: How library budget-setters respond to performance

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(1) (2) (3) (4) (5) (6) DV Total income Income from local govt Intercept 4.8 (0.039)*** 4.4 (0.048)*** 3.6 (0.58)*** 5.1 (0.039)*** 5.1 (0.045)*** 4.5 (0.51)*** Elasticity 0.28 (0.079)*** 0.60 (0.090)*** 0.54 (0.095)*** 0.18 (0.074)* 0.40 (0.08)*** 0.35 (0.086)*** Cutback t − 1 – 1.6 (0.098)*** 2.0 (0.09)*** – 0.15 (0.090) 0.48 (0.083) *** Elasticity × cutback t − 1 – -1.1 (0.19)*** -1.1 (0.19)*** – -0.85 (0.18)*** -0.79 (0.17)*** State FE No No Yes No No Yes Year FE No No Yes No No Yes S.E.s Clustered Clustered Independent Clustered Clustered Independent N 65309 65309 65309 63748 63748 63748 # unique libraries 6125 6125 6125 5975 5975 5975 R2 0.00015 0.0051 0.028 0.000074 0.00047 0.022 Notes: S.e.s in columns 1, 2, 4 and 5 are clustered by library. *** p < 0.001; ** p < 0.01; * p < 0.05. Outlier library-years, in which the library received a more than 33% budget increase or budget cut, or library-years with an elasticity of absolute value more than 2 are excluded.

The first column shows that indeed, budgets are increased more when a library’s short-run elasticity is high. A one standard deviation increase in elasticity (by 0.46) is associated with an approximately one-and-a-third standard deviations change to the budget increment. The second and third columns include a dummy variable for a cutback year in t − 1, and interact this with elasticity measure. After cutback years, the effect of elasticity is significantly less than after a normal year, as predicted by the theory; indeed, it is significantly negative, so that when an initial cut has a large effect on output, then there is a smaller subsequent budget increase on average. The third column includes state and year fixed effects. Columns 4-6 repeat the analysis, but use percentage change in local government funding as the dependent variable, with broadly similar results.10

Extension: monitoring the bureaucracy When the cost of funds are high enough to rule out temporary spending increases, governments may seek alternative ways to control the bureaucracy. To see this, suppose that by paying a monitoring cost m, the government can ensure that the bureaucracy produces at its efficient level y = ατ + βτ x in period 1. For instance, certain budget items may be ring-fenced, harming the bureaucracy’s flexibility in responding to changing circumstances but simultaneously forcing it to cut the fat, not the muscle. Or, ex post checks may be used to discover and sanction inefficient spending patterns. This will be unnecessary when x1 ≥ x, ¯ but will be worthwhile for high enough k. For, when both types produce efficiently, there are two benefits – first a period one benefit, reflecting the extra productivity of a low 10 The

“cutback in t − 1” dummy is still defined with reference to total funding, as the logic of the theory requires.

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type bureaucracy that is prevented from pooling; second, the indirect benefit from learning the types and allocating resources efficiently in period two. Specifically, after paying the monitoring cost, the government can choose x1 = x1∗ . Each type of bureaucracy then produces efficiently in round 1, and the government can then correctly distinguish the type it faces, resulting in round 2 allocations of xH or xL . On the other hand, without monitoring, the government’s payoff is given by (1) with x1 set to xˆ1 . If the monitoring cost is not too high, and if the credit crisis is sufficiently serious (k is high), then the government will always prefer to monitor.11

Conclusion To enhance our understanding of the dilemmas of spending cuts, this paper developed a simple theory in which government is uncertain about the effect of changing a department’s budget. The theory predicts that less efficient departments will be more affected by budget cuts, since they “pool” with more efficient departments so as to exaggerate the effect of their loss. This prediction was confirmed in a sample of US libraries. It was also confirmed that budget-setters are less reactive to short-run estimates of the budget-output slope in the year after a budget cut. It is worth reiterating this theory’s domain of application. The argument applies to bureaucracies whose output is measurable in the short term – so, for example, probably not to arts organizations, whose output is not easily measurable, nor to long-term infrastructure projects or investments whose impact is not immediately 11 Proved

in the Appendix.

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visible. Also, the assumption of a budget-maximizing bureaucracy implies that bureaucratic rewards cannot be directly linked to performance; in other words, contracts are incomplete. Incomplete contracts are a common theme in political economy. Nevertheless, governments in many developed countries have invested heavily in measuring and rewarding bureaucratic performance, and where this is successful, the information problem will no longer bite. Conversely, the Washington Monument ploy need not be limited to politics; the same behaviour may arise within firms. It would be interesting to find examples. The practical implication of this paper is straightforward: reforms and cuts do not mix, because cuts exacerbate the informational problems between government and the bureacracy. There may, nevertheless, be other ways in which spending crunches ease the path of public service reform. For example, they may increase electoral support for tough austerity measures. In the coming few years, as Western governments’ spending cuts take effect, there should be many opportunities for further research in this area.

Appendix Proof that (2) is negative and decreasing in δ and k. Write (2) as δ [βH (x¯ − xˆ1 ) − k

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Z x¯ xˆ1

c0 (x)dx].

By the FOC on xˆ1 , c0 (xˆ1 ) = βH /k and so by c00 > 0, the above is less than

δ [βH (x¯ − xˆ1 ) − k

Z x¯ βH

dx]

k

xˆ1

= δ [βH (x¯ − xˆ1 ) − βH (x¯ − xˆ1 )] = 0.

That (2) decreases without bound in δ is then immediate. To show it decreases in ¯ and x1 for the solution k, suppose k¯ > k. Write x¯1 for the solution to c0 (x) = βH /k, to c0 (x) = βH /k. Observe that x¯1 < x1 Then for k, (2) is B ≡ δ [βH (x¯ − x1 ) − k

Z x¯

c0 (x)dx],

x1

while for k¯ it is

δ [βH (x¯ − x¯1 ) − k¯

Z x¯

c0 (x)dx]

x¯1

= δ [βH (x¯ − x1 + x1 − x¯1 ) − k = B + δ [βH (x1 − x¯1 ) − k

Z x 1

Z x¯

0

c (x)dx − k

Z x 1

0

c (x)dx − (k¯ − k)

x¯1

x1

c0 (x)dx − (k¯ − k)

x¯1

Z x¯

c0 (x)dx]

x¯1

Z x¯

c0 (x)dx].

x¯1

Of the terms in square brackets, the first two sum to less than zero since c0 (x1 ) = βH /k and c00 > 0, and the last term is negative. Lastly observe that as k → ∞, xˆ1 → 0 and (2) therefore approaches δ [βH x¯ − kc(x)] ¯ which decreases towards infinity with k. QED

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Proof that when m is not too high and k is sufficiently high, the government will prefer to monitor Specifically, the condition is m < (1 − π)(αL − αH ). The government’s total payoff after paying to monitor is: −m+δ [π(αH +βH x1∗ )+(1−π)(αL +βL x1∗ )−kc(x1∗ )]+π(yH −c(xH ))+(1−π)(yL −c(xL )). (3) Comparing (1) to (3) shows the government prefers to monitor if

m < B1 + B2 ,

where B1 represents the period 1 benefit of monitoring and B2 the period 2 benefit: B1 = δ [π(αH + βH x1∗ ) + (1 − π)(αL + βL x1∗ ) − (αH + βH xˆ1 ) − k[c(x1∗ ) − c(xˆ1 )]]; B2 = π(βH (xH − x2∗ ) − [c(xH ) − c(x2∗ )]) + (1 − π)(βL (xL − x2∗ ) − [c(xL ) − c(x2∗ )]).

B2 is easily seen to be positive since xH and xL are optimal for a high and low type respectively. B1 can be split into two components. First there is the value from preventing pooling, thus increasing the productivity of the low type. Second there

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is the benefit of being able to choose an ex ante optimal budget. Thus B1 = δ [π(αH + βH x1∗ ) + (1 − π)(αL + βL x1∗ ) − kc(x1∗ ) −{π(αH + βH xˆ1 ) + (1 − π)(αL + βL xˆ1 ) − kc(xˆ1 )} +{π(αH + βH xˆ1 ) + (1 − π)(αL + βL xˆ1 ) − kc(xˆ1 )} −(αH + βH xˆ1 − kc(xˆ1 )]

The first two lines are the benefit of choosing an optimal x1 . They sum to a positive amount since x1∗ is the optimal choice when types are unknown, and therefore maximizes π(αH + βH x) + (1 − π)(αL + βL x) − kc(x). The last two lines are the benefit of preventing pooling. They simplify to

(1 − π)(αL − αH + (βL − βH )xˆ1 )

Now, as k grows large xˆ1 → 0 and this term approaches (1 − π)(αL − αH ). Thus if m < (1 − π)(αL − αH ), for k large enough the government will find it worthwhile to monitor.

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Reconstructing an Instrumental Model.” British Journal of Political Science 15(3):299–328. ArticleType: research-article / Full publication date: Jul., 1985 c 1985 Cambridge University Press. / Copyright URL: http://www.jstor.org/stable/193696 Hood, C. and M. Wright. 1982. “Big government in hard times.” Public administration p. 109. Independent. 2009. “Clinton: ’Never waste a good crisis’ - Americas, World The Independent.” The Independent . Niskanen, W. A. 1971. “Bureaucracy and representative government.”. Seib, Gerald F. 2008. “In Crisis, Opportunity for Obama.” wsj.com . URL: http://online.wsj.com/article/SB122721278056345271.html USAToday. 2009. “Obama: Crisis is time of ’great opportunity’ - USATODAY.com.” USA Today . Wildavsky, A. 1964a. The politics of the budgetary process. Little, Brown and Co. Wildavsky, A. 1964b. The politics of the budgetary process. Little, Brown and Co. Wood, Elizabeth J. and Victoria L. Young. 1988. Strategic marketing for libraries. Greenwood Publishing Group.

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